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arXiv · 2312.04697

Geometric Analysis of the Generalized Surface Quasi-Geostrophic Equations

Martin Bauer·Patrick Heslin·Gerard Misiołek·Stephen C. Preston
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Abstract

We investigate the geometry of a family of equations in two dimensions which interpolate between the Euler equations of ideal hydrodynamics and the inviscid surface quasi-geostrophic equation. This family can be realised as geodesic equations on groups of diffeomorphisms. We show precisely when the corresponding Riemannian exponential map is non-linear Fredholm of index 0. We further illustrate this by examining the distribution of conjugate points in these settings via a Morse theoretic approach.

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Martin Bauer, Patrick Heslin, Gerard Misiołek, Stephen C. Preston. 2023-12-07. Geometric Analysis of the Generalized Surface Quasi-Geostrophic Equations. https://arxiv.org/abs/2312.04697

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